Ayesha Sohail

Hall Effect on Falkner—Skan Boundary Layer Flow of FENE-P Fluid over a Stretching Sheet

The Falkner—Skan boundary layer steady flow over a flat stretching sheet is investigated in this paper. The mathematical model consists of continuity and the momentum equations, while a new model is proposed for MHD Finitely Extensible Nonlinear Elastic Peterlin (FENE-P) fluid. The effects of Hall current with the variation of intensity of non-zero pressure gradient are taken into account. The governing partial differential equations are first transformed to ordinary differential equations using appropriate similarity transformation and then solved by Adomian decomposition method (ADM). The obtained results are validated by generalized collocation method (GCM) and found to be in good agreement. Effects of pertinent parameters are discussed through graphs and tables. Comparison with the existing studies is made as a limiting case of the considered problem at the end.

A review on hyperthermia via nanoparticle-mediated therapy

Hyperthermia treatment, generated by magnetic nanoparticles (MNPs) is promising since it is tumour-focused, minimally invasive and uniform. The most unique feature of magnetic nanoparticles is its reaction and modulation by a magnetic force basically responsible for enabling its potential as heating mediators for cancer therapy. In magnetic nanoparticle hyperthermia, a tumour is preferentially loaded with systemically administered nanoparticles with high-absorption cross-section for transduction of an extrinsic energy source to heat. To maximize the energy deposited in the tumour while limiting the exposure to healthy tissues, the heating is achieved by exposing the region of tissue containing magnetic nanoparticles to an alternating magnetic field. The magnetic nanoparticles dissipate heat from relaxation losses thereby heating localized tissue above normal physiological ranges. Besides thermal efficiency, the biocompatibility of magnetite nanoparticles assisted its deployment as efficient drug carrier for targeted therapeutic regimes. In the present article, we provide a state-of-the-art review focused on progress in nanoparticle induced hyperthermia treatments that have several potential advantages over both global and local hyperthermia treatments achieved without nanoparticles. Green bio-nanotechnology has attracted substantial attention and has demonstrable abilities to improve cancer therapy. Furthermore, we have listed the challenges associated with this treatment along with future prospective that could attract the interest of biomedical engineers, biomaterials scientists, medical researchers and pharmacological research groups.

NUMERICAL MODELING OF CAPILLARY–GRAVITY WAVES USING THE PHASE FIELD METHOD

In this paper, we present a numerical model based on the widely used finite element formulation to analyze in detail the effect of surface active agents on capillary–gravity wave parameters such as phase velocity and wave amplitude. Moreover, the effect of a physicochemical parameter, which is the ratio of surface concentration to surface tension is also considered. For a number of fluid samples covering a range of concentrations from 0 to 0.01 molar, the phase speed of waves propagating on the surface of the liquid is found to decrease monotonically as the concentration of the solution considered is increased up to a limit of 0.004 molar. This is attributed to the corresponding increase in capillary number. It is shown numerically that the Marangoni effects contribute to the interfacial dynamics for fluid with physicochemical parameter value greater than 0.5. Moreover, a grid refinement study shows accuracies and convergence orders of the numerical model.

Comparison of optimal homotopy analysis method and fractional homotopy analysis transform method for the dynamical analysis of fractional order optical solitons

In this article, dynamical analysis of fractional order Schrödinger equation governing the optical wave propagation is reported in detail. The validity criteria for the application of the semi-analytic asymptotic methods are exploited. Comparison between the solutions obtained by the two asymptotic techniques, that is, the fractional homotopy analysis transform method and the optimal homotopy analysis method is performed to select the most accurate technique for the stated problem.

Numerical Study of Free Convective Flow of a Nanofluid over a Chemically Reactive Porous Flat Vertical Plate with a Second-Order Slip Model

AbstractA mathematical model for free convective boundary-layer flow of a nanofluid with second-order velocity slip over a permeable vertical flat plate has been presented. The system of governing equations is first nondimensionalized, and then similarity transformations are used to convert the governing partial differential equations into a set of coupled ordinary differential equations. A numerical algorithm is applied to this boundary value problem (BVP) of coupled ordinary differential equations. Collocation method is used for the solution of the nonlinear ordinary BVP. The dimensionless analysis revealed that the dimensionless field variables (velocity, temperature, and nanoparticle volume fraction), and the flow characteristics (skin friction factor, heat transfer, and nanoparticle volume fraction transfer) in the respective boundary layers depend on the Prandtl number (Pr), the Lewis numbers (Le), the thermophoresis parameter (Nt), the Brownian motion parameter (Nb), the buoyancy ratio parameter (N...

Dynamical Study of Fractional Order Tumor Model

In this paper, we have studied the fractional order model of tumor cells growth and their interactions with general immune effector cells, by using multi-step generalized differential transform method (MSGDTM). We discussed this nonlinear model because it differs from most others in the literature. It takes into account (i) the infiltration of the tumor by CTLs (cytotoxic T lymphocytes) and (ii) the possible effects of effector cell inactivation. The approximate solutions obtained by MSGDTM are highly accurate and valid for a longer period of time.

Painlevé property and approximate solutions using Adomian decomposition for a nonlinear KdV-like wave equation

In this paper, we have discussed the integrability of a nonlinear partial differential equation, with a focus on the Painleve property, the compatibility condition and the Backlund transformation. Afterwards, the Adomian decomposition method, which accurately computes the series solution, has been used to obtain an approximate solution. The convergence analysis based on the wave number and nonlinearity parameter has also been performed using graphical interface of a numerical solver.

Numerical analysis of fractional-order tumor model

In this paper, the tumor-immune dynamics are simulated by solving a nonlinear system of differential equations. The fractional-order mathematical model incorporated with three Michaelis–Menten terms to indicate the saturated effect of immune response, the limited immune response to the tumor and to account the self-limiting production of cytokine interleukin-2. Two types of treatments were considered in the mathematical model to demonstrate the importance of immunotherapy. The limiting values of these treatments were considered, satisfying the stability criteria for fractional differential system. A graphical analysis is made to highlight the effects of antigenicity of the tumor and the fractional-order derivative on the tumor mass.

Embodied modeling approach to explore tumour cells drug resistance

Mathematical modelling provides mechanistic insight of an infirmity by emulating the course of disease on individual or group level under various interventions and hence makes pragmatic contribution to complement conventional biomedical research modalities. Subsequently, real-world effectiveness is observed in the prediction of experimental outcome that leads to optimized clinical therapies. This article addresses with the aid of mathematical modelling, the drug pharmacokinetic-pharmacodynamic along with treatment responses. This article uses an agent based model to discuss the effects of chemotherapy on angiogenesis as well as tumor microenvironment and establishes pertinency between numerical and experimental results. This study supports the emerging “discrete analysis ” which, in the near future, is anticipated to be a promising major tool, for designing rational dosage regimes and effective dosage forms.

Analysis of a channel and tube flow induced by cilia

Power law metachronal wave motion, responsible for the cilia transport is investigated in this paper using numerical tools. The dynamical analysis is made in channel and in tube to demonstrate the quantitative effect of the geometry. Similarity transformations are employed to convert the governing partial differential equations into a set of coupled ordinary differential equations. A swift and accurate collocation algorithm is applied to the boundary value problem (BVP) of coupled ordinary differential equations. A nondimensional graphical analysis of the waving amplitude is reported by varying the flow consistency and flow behavior indices.